How Mathematicians wonder: The Riemann hypothesis

The Riemann hypothesis [the tiny photo here shows Riemann, he who hypothesized] fascinates an uncountable number of mathematicians. Many have tried, tried, tried to prove that it’s true. The problem is not easy. Here’s proof, of a sort, of how not easy it is. The following passage appears on page 100 of Ricardo Perez Marco [pictures here in a photo larger than the miniature of Riemann]’s treatise called Conclusion and comments on the Riemann Hypothesis” [Jornadas Sobre los Problemas del Milenio, Barcelona, del 1 al 3 de junio de 2011]:

Is it true? The first question one has to ask about an open conjecture is if we do actually believe it. In the case of the Riemann Hypothesis there seems to be an overwhelming opinion in favor of it. And this, despite that the vast majority of mathematicians that have an opinion don’t have a clue on how to go about it. Also despite some notable exceptions of unbelievers. Indeed, it appears that some of the best specialists that have spend [sic] considerable considerable effort into it, at the end of their life start to become skeptic. We can just mention the best known of them, J.E. Littlewood [deviser of Littlewood’s Law of Miracles]. At first this seems quite troubling. But knowing human nature, probably we can only take this as another indication that the Riemann Hypothesis is certainly true. One can notice that most (all?) of the attempts to resolve the questions have tried to prove and not disprove it. The only attempts to disprove it seem to have been numerical. We will not even discuss the possibility of the Riemann Hypothesis to be non-decidable: It is obviously a genuine well posed beautiful problem.

(Thanks to investigator Lieven Lebruyn for bringing this to our attention.)